Models (3) and (4) are variations of model (1) . Model (3) scales the basic height-diameter 

 curves by the stand's site index, while model (4) also allows a site index related shift in 

 the form of the height-diameter curve. Model (5) is a form of model (2) in which the basic 

 height-diameter curve is scaled by site index. In applying these models to diameter classes, 

 the dependent variable was defined as the average height of the Dth diameter class for a stand 

 with site index of S. 



To fit models (3), (4), and (5) to the uneven-aged height data, they were first transformed 

 by use of natural logarithms to the following: 



In(Hj^-4.5) = f 1 + f2-lnS + f3-(D+K)""' (6) 



In(Hp-4.5) - gi + g2lnS + • S • (D+K) ""^ (7) 



2 



in(Hp-4.5) = hi + h2lnS + h-^lnU + ht,(inS) (8) 



For models (6) and (7), screening runs were then made with values of K ranging from 0.0 to 

 40.0 and values of m ranging from 0.1 to 4.0. Model (8) was fitted using a single least 

 squares regression run. The three models were then tabulated over D and S to check for reason- 

 ableness of behavior, their residuals were plotted over predicted average height to determine 

 homogeneity of variance, and the residuals were also examined for normality. The final model 

 form selected was (6) with K = 35.0 and n = 2.0. The residuals about this model were normally 

 distributed with homogeneous variance, and therefore the lognormal bias correction proposed 

 by Oldham (1965) and Baskerville (1972) could be used. This correction consisted of adding 

 one-half the mean-squared error (0.030203189) to the intercept of model (6) and then taking 

 the antilog of model (6) to obtain the final uneven-aged height model. As an index of fit, 

 the RMSQR for the final log model was 0.1270. 



88 



